{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Recognizing Manifolds\n", "\n", "This is about combinatorial topology in [polymake](https://polymake.org) from within [Oscar](http://oscar-system.org) (via [Polymake.jl](https://github.com/oscar-system/Polymake.jl)).\n", "\n", "Author: [Michael Joswig](https://page.math.tu-berlin.de/~joswig/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " ----- ----- ----- - ----- \n", "| | | | | | | | | | \n", "| | | | | | | | \n", "| | ----- | | | |----- \n", "| | | | |-----| | | \n", "| | | | | | | | | | \n", " ----- ----- ----- - - - - \n", "\n", "...combining (and extending) ANTIC, GAP, Polymake and Singular\n", "Version\u001b[32m 0.6.0 \u001b[39m... \n", " ... which comes with absolutely no warranty whatsoever\n", "Type: '?Oscar' for more information\n", "(c) 2019-2021 by The Oscar Development Team\n" ] }, { "data": { "text/plain": [ "Polymake" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Oscar\n", "const pm = Polymake" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Casella and Kühnel, Topology 40 (2001), found a 16-vertex triangulation of a K3 surface, and this is the minimum number. While there are many K3 surfaces which are distinct as algebraic varieties, topologically they are all the same." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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